# Plots the binomial density for four different values of N. # Figure caption: The pdf of the binomial mean X-bar when p = 0.4 # for four different values of n. As n increases, the # distribution becomes concentrated (the standard deviation of the # sample mean becomes small), with the center of the distribution # getting close to muX = 0.4 (the LLN). In addition, the # distribution becomes approximately normal (the CLT). # Set up the graphics device. par(mfrow = c(2, 2)) par(mar = rep(3, 4)) # Set up the binomial parameters. p <- 0.4 n.values <- c(5, 10, 20, 50) for (i in 1:4) { n <- n.values[i] x.values <- 0:n means <- x.values / n plot(means, dbinom(x.values, n, p) xlim = c(0,1), main = "", xlab = "", ylab = "", xaxt = "n", yaxt = "n", bty = "n", pch = 16, cex = 0.7) axis(1, at = seq(from = 0, to = 1, by = 0.2), cex.axis = 1.4) } dev.print(device = postscript, "6.1.png", horizontal = TRUE)